1. If \(u_i=\cfrac{x_i-35}{10}\), \(∑f_i u_i=30\), and \(∑f_i=60\), then determine the value of \(\bar{x}\).

2. If \(u_i = \cfrac{x_i − 35}{10}\), \(Σf_i u_i = 30\), and \(Σf_i = 60\), then find the value of \(\bar{x}\).

3. If \(u_i = \frac{x_i - 30}{10}\), \(∑f_i = 50\), and \(∑u_i f_i = 25\), then what is the value of \(\bar{x}\)?

4. If \(u_i = \frac{x_i − 35}{10}\), \(Σf_iu_i = 30\), and \(Σf_i = 60\), then find the value of \(\bar{x}\).

5. If \(u_i=\cfrac{x_i−35}{10} , Σf_iu_i=30\), and \(Σf_i=60\), then determine the value of \(\bar{x}\).

6. If \(∑f_i(x_i - a) = 400\), \(∑f_i = 50\), and \(a\) (assumed mean) = 52, then the value of the combined mean \(\bar{x}\) is –

(a) 52 (b) 60 (c) 80 (d) 90

7. If \(u_i = \cfrac{x_i - 25}{10}\), \(\sum f_i u_i = 20\), and \(\sum f_i = 100\), then what is the value of \(\bar{x}\)?

8. If \(∑f_i d_i = 400\), \(∑f_i = 50\), and \(a =\) assumed mean \(= 52\), then the value of the combined mean is –

(a) 52 (b) 60 (c) 80 (d) 55

9. If \(u_i = \cfrac{x_i - 20}{10}\), \(\sum{f_iu_i} = 15\), and \(\sum{f_i} = 80\), then what will be the value of \(\bar{x}\)?

(a) 21.875 (b) 20.875 (c) 21.800 (d) 20.125

10. If \(u_i=\cfrac{x_i−35}{10} , Σf_iu_i=30\) and \(Σf_i=30\), find the value of \(\bar{x}\).

11. If \(u_i =\cfrac{x_i - 25}{10}\), \(\sum f_i u_i = 20\), and \(\sum f_i = 100\), then find the value of \(\bar{x}\).

12. If the mean of a statistical distribution is 4.1, \(∑f_i x_i = 132 + 5k\), and \(∑f_i = 20\), then what is the value of \(k\)?

13. If the mean of a frequency distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then find the value of \(k\).

14. If the mean of a frequency distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then find the value of \(k\).

15. If the mean of a frequency distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then find the value of \(k\).

16. Here’s the English translation: *If the mean of a statistical distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then what is the value of \(k\)?* Would you like help solving it too? I’d be glad to walk through it with you.

17. If \(\cfrac{p}{q} = \cfrac{5}{7}\) and \(p - q = -2\), then the value of \(p + q\) is –

(a) 12 (b) 13 (c) 14 (d) 15

18. If \(\theta\) is a positive acute angle and \( \sin \theta - \cos \theta = 0 \), then the value of \(\cot 2\theta\) is –

(a) \(\cfrac{1}{√3}\) (b) 1 (c) √3 (d) 0

19. If the equation \(3x^2 - 6x + p = 0\) has real and equal roots, then the value of \(p\) is –

(a) \(\cfrac{5}{3}\) (b) -\(\cfrac{1}{3}\) (c) -3 (d) 3

20. If \(\sum f_iu_i = 10\), class width = 20, \(\sum f_i = 40 + k\), the combined mean is 54, and the assumed mean is 50, then what is the value of \(k\)?

21. If \( u_i = \frac{x_i - 45}{10} \), \( ∑f_i u_i = -16 \), and \( ∑f_i = 200 \), then what is the value of \( \bar{x} \)?

22. If \(m+n = \sqrt{13}\) and \(m-n = \sqrt{5}\), then the value of \(mn\) is –

(a) 2 (b) 18 (c) 9 (d) 8

23. If the mean of a statistical distribution is **4.1**, \(∑f_i.x_i = 132+5k\), and \(∑f_i=20\), determine the value of \(k\).

24. If \( u_i=\cfrac{x_i−35}{10} \), \( Σf_iu_i=30 \), and \( Σf_i=60 \), then determine the value of \( \bar{x} \).

25. The mean of a statistical distribution is 4.1. Given that \(∑f_i.x_i = 132 + 5k\) and \(∑f_i = 20\), find the value of \(k\).

26. The mean of a statistical distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\). Find the value of \(k\).